Your card will work with the system since the connection you will be using is still PCIex16 2.0. I used to have a GTX 560Ti on a Asus P5Q motherboard and a Core 2 Quad Q8200 with 4GB of DDR2 RAM. All of which worked flawlessly no hitch whatsoever.
However you wont be able to get the full capacity of your HD 6970. Your CPU will bottleneck your performance due to games and other applications may require a higher capacity CPU. For example my current build has a i7 920 at the same clocks as the C2Quad Q8200 assassin's creed brotherhood runs at 70FPS compared to 30FPS. I agree with amuffin the only question is would your PSU handle the load of the HD 6970.